Bus1Ban Business Economics And Data Assessment Answers

Section A: Basic Analysis
1.What proportions of the students in your sample are domestic students and what proportion are international? 
2.What is the relationship between price and estimated average weekly consumption of beverages by students in your sample? 
3.Summarise the beverage preferences for your sample of students. What are the most popular and least popular beverages? 
4.Will price affect preference?
Section B: The behavior of domestic students vis-à-vis international students
5.How does the demand (price-quantity relationship) of international students differ from that of domestic students in your sample? 
6.Compare the distribution of beverage preferences for domestic and international students. What are the most and least popular beverages for students in each group? 
7.Does price influence choice of beverage for domestic students more than for international students? 
Section C: Advance scenarios
8.Suppose, you randomly selected a student from the 2015 BUS1BAN class.  
a.How likely is it that the student will be a domestic student and how likely is it that the student will be an international student? Provide interval estimates and interpret your results. 
b.How likely is it that the student will choose soft drink (Pepsi, Coke etc.) as their first preference? Provide interval estimates and interpret your results. 
c.What is the probability that the student will choose tea/coffee as their second preference if he/she selected soft drink (Peps, Coke etc.) as the first preference?

Introduction

The present assignment is an investigation into the beverage drinking habit of the students of BUS1BAN course. The consumption pattern of 5 different beverages is investigated. A sample of 75 students is drawn randomly from the BUS1BAN Class of 2015. Both domestic and international student’s beverage consumption vis-a-vis price, discount, preference is studied in the present assignment.

Data Analysis

Section A: Basic Analysis

Answer 1. 

A study of the students origin shows that the number of International Students = 7

And the number of Domestic Students = 69

The total sample size of the students = 75

Hence, the proportion of international students in the sample =

Hence, the proportion of domestic students in the sample =

Answer 2. 

An analysis of the estimated average weekly consumption based on prices of the beverages for the sample can be shown by the following table:

Table 1: Relation between Estimated Weekly Consumption based on price

Price	Estimated Average Consumption
$0.50	12.147
$1.00	9.733
$1.50	7.840
$2.00	6.013
$2.50	4.827
$3.00	3.733
$3.50	3.013
$4.00	2.080
$4.50	1.387
$5.00	0.893

The investigation of the estimated weekly consumption and average beverage consumption shows that there is a linear relationship between the two variables. The estimated average weekly consumption of beverage decreases with increase in price from $0.50 to $5.00.

Answer 3. 

The beverage preference of the selected sample can be shown as:

Table 2: Preference level of beverages of the sample

Preference Level	Soft drinks (Coke/Pepsi etc.)	Fruit Juice	Tea /coffee	Energy drinks	Other (water, milk drinks etc.)
First Preference	12	7	12	4	40
Second Preference	12	19	24	3	17
Third Preference	11	29	13	9	13
Fourth Preference	28	17	13	15	2
Last Preference	12	3	13	44	3

An investigation into the beverage preference of the selected sample of students shows that Others (water, milk drinks etc.,) is preferred by 40 of the 75 students as their first preference. The second most preferred beverage of the students is Tea / coffee. The third most popular beverage Fruit Juice. The least popular beverage is Energy drink, preferred by 44 students)

Answer 4. 

To test whether the discount in price of beverage would change the preference of the sampled students a one-way ANOVA is done.

• The NULL hypothesis : The Average preference would not change with increase in discount
• The Alternate hypothesis : The Average preference would change with increase in discount
• Decision rule: Table value for 2, 222 degrees of Freedom from F-table value is 16.503 at 0.05 level of significance. Thus, reject Null hypothesis if F-critical value is more than 2.68.

Table 3: ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	6.907	2.000	3.453	16.503	0.000	3.037
Within Groups	46.453	222.000	0.209
Total	53.360	224.000

From the ANOVA we find that F-table value (16.503) is more than the F-crit (3.037) value. In addition, the p-value (0.000) is less than the significance level of 0.05. Hence, we reject the Null hypothesis. Thus, we can find that with change in discount on beverage, the preference of the students also changes.

Section B: Behavior of Students

Answer 5. 

The demand of beverages of Domestic vs International Students vis-à-vis price can be shown as:

Table 4: Demand of Domestic and International Students

	$0.50	$1.00	$1.50	$2.00	$2.50	$3.00	$3.50	$4.00	$4.50	$5.00
Domestic Student	852	675	544	417	333	255	209	145	95	60
International Student	43	37	27	6	8	7	9	4	2	1

From the above table we find that for both domestic as well as international students demand decreases as the price increases.

Answer 6. 

Table5: Preference of Drinks of Domestic and International Students

Preference	Soft Drinks		Fruit Juice		Tea / Coffee		Energy Drinks		Others
	D	I	D	I	D	I	D	I	D	I
First	12	0	6	1	12	0	4	0	34	6
Second	12	0	15	4	21	3	3	0	17	0
Third	10	1	27	2	11	2	8	1	12	1
Fourth	24	4	17	0	12	1	13	2	2	0
Last	10	2	3	0	12	1	40	4	3	0

• D – Domestic
• I – International

The preference of beverage of domestic and international students are shown in Table 5. For the domestic students we find that the most preferred beverage is Others (34) and the least preferred beverage is Others (3). For international students the most preferred beverage is Others (6), while the least preferred beverage Fruit Juice and Others (0).

Answer 7. 

The average consumption of different beverages by domestic and international students can be represented as

Table 6: Average Consumption of beverages of Domestic and international students

	$0.50	$1.00	$1.50	$2.00	$2.50	$3.00	$3.50	$4.00	$4.50	$5.00
Domestic Student	13	10	8	6	5	4	3	2	1	1
International Student	8	8	6	5	4	4	2	2	1	1

From the above table we find that as the price of beverage increases the demand / consumption of beverages decreases for both domestic as well as international students. In addition, above the price $4.00 the average demand for beverages for both domestic as well as internationals students is the same.

Section C: Advanced Scenario

Answer 8. 

Part A

The 2015 class of BUS1BAN had 551 students. In addition the number of Domestic Students was 498 and International students were 53.

The 95% confidence interval for population proportion is given by

where, p is the population proportion (Domestic or International Student)

z_c is the confidence interval (for 95% confidence interval z_c = 1.96)

n is the population size = 551

Hence the 95% confidence interval for the proportion of Domestic students can be calculated as:

The proportion of domestic students =

Thus the 95% confidence interval for domestic students is =  

Thus the interval estimate of the domestic students of 2015 BUS1BAN Class

= 0.879 to 0.929 with a mean of 0.904

Hence the 95% confidence interval for the proportion of International students can be calculated as:

Thus the proportion of international students

The 95% confidence interval for international students is=

Thus the interval estimate of the international students of 2015 BUS1BAN Class

= 0.071 to 0.121 with a mean of 0.096

Hence, the 95% confidence Interval can be interpreted as: If another class of the year 2015 is selected then with a 95% confidence it can be said that the proportion of Domestic students would lie within the range of 0.879 to 0.929. Similarly, for another class of 2015 with a 95% confidence interval it can be said that the proportion of International Students would lie within the range of 0.071 to 0.121.

Part B

For the BUS1BAN Class of 2015 the number of students who have soft drink (Coke, pepsi) as their first preference = 81

Hence, the proportion of students who’s first preference is soft drink

Thus, the 95% confidence interval for first preference soft drink

Thus the 95% confidence interval for first preference soft drinks for the class of BUS1BAN of 2015 is 0.118 to 0.176 with a mean of 0.147

Thus, the 95% confidence Interval can be interpreted as: If another class of the year 2015 is selected then with a 95% confidence it can be said that the proportion of students whose first preference would be soft drinks would lie within the range of 0.118 to 0.176.

Part C

For the BUS1BAN Class of 2015 the number of students who have tea / coffee as their second preference = 147

Hence, the proportion of students who’s second preference is tea / coffee =

Thus, the 95% confidence interval for second preference tea / coffee

Thus the 95% confidence interval for second preference tea / coffee for the class of BUS1BAN of 2015 is 0.23 to 0.304 with a mean of 0.267

Thus, the 95% confidence Interval can be interpreted as: If another class of the year 2015 is selected then with a 95% confidence it can be said that the proportion of students whose second preference would be tea / coffee would lie within the range of 0.23 to 0.267.

Answer 9. 

From my sample data I find that the number of students whose first preference is soft drinks = 16.

Thus the proportion of La Trobe students whose first preference is soft drinks =

To test the claim made by La Trobe University that for 25% of the students the first preference is soft drinks, the hypothesis for testing of proportions is used

The Null hypothesis is

The Alternate hypothesis is

The test hypothesis is given by  

where,  is the sample proportion whose first preference is soft drinks = 0.213.

is the test proportion = 0.25

n is the sample size = 100

Hence,  

For z-value – 0.855 the p-value is 0.196

At 1%, 5% and 10% level of significance the z-value is more than the samples’ z-value. Hence we have enough evidence to reject the Null Hypothesis. Hence, at 1%, 5% and 10% the claim made by La Trobe University regarding the consumption of Soft drinks is true.

Answer 10. 

From the sample of the 2015 class of BUS1BAN we find that there are 68 domestic students.

68 domestic students in a week consume 277 beverage cans

Hence 10, 000 domestic students would consume   

From the sample of the 2015 class of BUS1BAN we find that there are 7 international students.

7 international students in a week consume 10 beverage cans in a week

Hence 15, 000 international students would consume   

The analysis of the sample showed that there were more domestic students than international students. The study found that the consumption of beverage decreases as the prices of the beverage increases. Moreover, it is found that for the sample Others is the most preferred drink of the maximum number of students. In addition, Fruit Juice and others is the least referred drink. In addition, it is also found that with an increase in discount percentage the preference of the beverage would also change.

In addition it is found that at 1%, 5%, 10% level of significance, more than 25% of the students of La Trobe University prefer soft drinks.

The fault with the present sampling technique is in the selection process. The present takes the Class BUS1Ban of 2015 for the whole of La Trobe University. To remove the sampling error the survey should be open to La Trobe University students.

In addition, there may be seasonal variation in beverage preference from summer to Winter. This seasonal preference has not been taken into consideration.